If you start a biology experiment with5000000 cells and 25% of the cells are dying every minute, how long with it be before there are fewer than 1000 cells?
1000 ≤ 5000000(1 - .25)^n
ln(1000) ≤ ln(5000000) + n ln(.75)
[ln(1000) - ln(5000000)] / ln(.75) ≤ n
30974552
Maths
Well, let's do the math! If 25% of the cells are dying every minute, that means we're losing 25% of the 5,000,000 cells every minute.
So, after the first minute, we're left with (5,000,000 - (25% * 5,000,000)) = 3,750,000 cells.
If we keep repeating this every minute, we can use some clown logic. It's like a clown losing nose after nose after nose... until the clown runs out of noses!
After 2 minutes, we're left with (3,750,000 - (25% * 3,750,000)) = 2,812,500 cells.
After 3 minutes, we have (2,812,500 - (25% * 2,812,500)) = 2,109,375 cells.
And so on...
Using this pattern, we can figure out how long it takes to have fewer than 1,000 cells. But don't worry, I won't make you wait through all those calculations. Let me do the magic behind the scenes...
*Taps clown shoes together*
Drumroll, please!
After approximately 93 minutes, you'll have fewer than 1,000 cells. That's a lot of cell losses! So, remember to treat your cells with care, just like a clown treats their rubber chickens!
To determine how long it will take for the number of cells to drop below 1000, we need to calculate the number of minutes that pass until the count reaches that threshold.
Let's break down the problem step by step:
1. We start with 5,000,000 cells.
2. Every minute, 25% of the cells die.
3. We want to know how long it takes until we have fewer than 1000 cells.
To solve this, we need to create an equation:
Number of cells at time 'T' = Starting number of cells - (Percentage of dying cells * Starting number of cells)^T
In this equation:
- 'T' represents the number of minutes.
- The percentage of dying cells is given as 25%, which in decimal form is 0.25.
- The starting number of cells is 5,000,000.
We need to find the value of 'T' when the number of cells drops below 1000.
Let's proceed:
Number of cells at time 'T' = 5,000,000 - (0.25 * 5,000,000)^T
Now, we can set up the inequality:
5,000,000 - (0.25 * 5,000,000)^T < 1000
Simplifying:
4,999,000 < (0.25 * 5,000,000)^T
To solve for 'T', we need to take the logarithm of both sides (base 0.25):
log base 0.25 (4,999,000) < T
Using a calculator, we find that log base 0.25 (4,999,000) is approximately 2.32.
Therefore, it will take approximately 2.32 minutes (or 2 minutes and 19 seconds) for the number of cells to drop below 1000 if 25% of the cells are dying every minute.